title: Artificial dispersion via high-order homogenization: magnetoelectric coupling and magnetism from dielectric layers.
abstract: We investigate a high-order homogenization (HOH) algorithm for periodic multi-layered stacks. The mathematical tool of choice is a transfer matrix method. Expressions for effective permeability, permittivity and magnetoelectric coupling are explored by frequency power expansions. On the physical side, this HOH uncovers a magnetoelectric coupling effect (odd-order approximation) and artificial magnetism (even-order approximation) in moderate contrast photonic crystals. Comparing the effective parameters' expressions of a stack with three layers against that of a stack with two layers, we note that the magnetoelectric coupling effect vanishes while the artificial magnetism can still be achieved in a centre-symmetric periodic structure. Furthermore, we numerically check the effective parameters through the dispersion law and transmission property of a stack with two dielectric layers against that of an effective bianisotropic medium: they are in good agreement throughout the low-frequency (acoustic) band until the first stop band, where the analyticity of the logarithm function of the transfer matrix ([Formula: see text]) breaks down.
authors.affiliation: CNRS, Ecole Centrale Marseille, Aix-Marseille Université, Institut Fresnel, UMR 7249, 13013 Marseille, France.
authors.forename: Yan
authors.initials: Y
authors.lastname: Liu
authors.forename: Sébastien
authors.initials: S
authors.lastname: Guenneau
authors.forename: Boris
authors.initials: B
authors.lastname: Gralak
keywords: Sophus Lie theorem; homogenization; magnetoelectric coupling; transfer matrix